1.2--Finding Limits Graphically & Numerically
Evaluate the following limits (if possible):
1)
lim f(x) =
x
2)
4
f(x)
lim f(x) =
x
2
2
3)
4
lim f(x) =
x
4)
0
f(2) =
Evaluate the following limits (if possible):
5)
6)
7)
8)
f(x) =
lim
x
5-
lim
x
x
2
lim
-
-3
f(x) =
+
f(x) =
lim f(x) =
x
0
1
1.2--Finding Limits Graphically & Numerically
Evaluate the following limits (if possible):
9)
lim
x
5
f(x) =
10) lim f(x) =
x
2
11) lim f(x) =
x
-3 -
12) lim f(x) =
x
-3
The Properties of Limits (p. 59) simply involve common
sense & are Algebra 1 related. It's better just to
work out problems to reinforce these concepts...
lim
x
0
sin x
x
=
1
This formula is on page 65.
It is
EXTREMELY important!!!
2
1.3--Finding Limits Analytically
1)
3)
5)
7)
lim
x
11
lim
x
7
9
lim
x
(x - 8)
2019
x2 - 4x - 45
lim
x
4x + 1
2x + 3
4
x2 - 2x - 63
2x + 8
5x2 - 80
2)
4)
6)
8)
x
lim
-8
lim
x
3
x2 - 15x + 36
x2 - 19x + 48
lim
5x3 + 2x2
lim
x2 - 4
x
x
(x2 + 4)
0
-2
x3 - 8x2
2x2 + x - 6
3
1.3--Finding Limits Analytically
9)
11)
13)
15)
x
lim
2.5
x
x
0
x
lim
17+
lim
-4
6x - 15
4 sin x
lim
x
8x3 - 125
-
lim
10)
x
lim
12)
(int x)
14)
(int x)
16)
5x - 19
3
x
x
x
0
lim
17-
lim
-5
-
8 sin 6x
3x
(int x)
x
x
4
1.3--Finding Limits Analytically
17)
x
lim
18)
f(x) =
31
x + 90 - 11
x - 31
f(x) =
lim
∆x
2
2
(x+∆x) + 3(x+∆x) - 5 - (x + 3x - 5)
0
∆x
5
1.3--Finding Limits Analytically
The SQUEEZE THEOREM, p. 65
(also called the "Sandwich Theorem")
g(x)
f(x)
h(x)
19)
Use the Squeeze Theorem to evaluate the following:
x2 sin ( 1
x )
0
lim
x
6
1.3--Finding Limits Analytically
(Textbook--page 68)
7